# How do you solve a/15=4/5?

Mar 27, 2018

color(teal)(a=12

#### Explanation:

Simply use cross multiplication $\ldots$
color(teal)(a/15=4/5

$\mathmr{and} ,$ color(teal)(5a=4*15

$\mathmr{and} ,$ color(teal)(a=(4*15)/5=4*3=12

hope that helped.

Mar 27, 2018

a = 12

#### Explanation:

Here, $\frac{a}{15} = \frac{4}{5}$
Or,$5 \cdot a$ = $15 \cdot 4$
Or,5a = 60
Or,a = $\frac{60}{5}$
Or,a = 12

Mar 27, 2018

$a = 12$

#### Explanation:

$\text{Alternatively multiply both sides of the equation by}$
$\text{the "color(blue)"lowest common multiple of 15 and 5}$

$\text{the lowest common multiple of 15 and 5 is 15}$

${\cancel{15}}^{1} \times \frac{a}{\cancel{15}} ^ 1 = {\cancel{15}}^{3} \times \frac{4}{\cancel{5}} ^ 1$

$\Rightarrow a = 3 \times 4 = 12$

Mar 27, 2018

$a = 12$

#### Explanation:

$\textcolor{b l u e}{\text{Important fact}}$

A fraction's structure is such that we have:

$\left(\text{numerators")/("denominators") color(white)("d")->color(white)("dd") ("count")/("size indicator of what is being counted}\right)$

You can not $\textcolor{p u r p \le}{\underline{\text{DIRECTLY}}}$ add, subtract or compare the 'counts' unless the 'size indicators' are the same.

Multiply by 1 and you do not change the value of something. However, 1 comes in many forms so you change the way something looks without changing its value.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

$\textcolor{g r e e n}{\frac{a}{15} = \left[\frac{4}{5} \textcolor{red}{\times 1}\right] \textcolor{w h i t e}{\text{dddd")->color(white)("dddd}} \frac{a}{15} = \left[\frac{4}{5} \textcolor{red}{\times \frac{3}{3}}\right]}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("dddd}} \frac{a}{15} = \frac{12}{15}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now that the bottom numbers or size indicators (denominators) are the same we can just compare the top numbers or counts (numerators).

Mathematically you say: multiply both sides by 15#

So we now have: $a = 12$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Check}}$

If we divide the left hand side by the right hand side we will get 1 if they are the same.

$\frac{12}{15} \div \frac{4}{5}$

$\frac{12}{15} \times \frac{5}{4}$

$\frac{5}{15} \times \frac{12}{4}$

$\frac{1}{3} \times \frac{3}{1} = 1$